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Lois Griffin, left, visits the doctor after agreeing to be a surrogate for her friends Naomi and Dale.

It is also an episode in which a central character finds herself with an unwanted pregnancy and contemplates an abortion, a subject that is frankly discussed  and flagrantly satirized  by the cartoon’s cast. The Fox network has said it will not broadcast “Partial Terms of Endearment,” which was produced for the 2009-10 season.

However, the home video arm of 20th Century Fox plans to release the episode as a stand-alone DVD in September, in packaging that plays up its polarizing qualities. When it does, many “Family Guy” fans will get their first look at an unlikely reminder of the television networks’ aversion to the issue of abortion, and a rare boundary encountered by an often rebellious series.

“Times really have changed,” said Seth MacFarlane, the creator of “Family Guy.” “The network is making a decision that is, unfortunately, probably based on people’s current ability to handle and dissect controversial narratives.”

As a longtime admirer of the comedies of Norman Lear  to the point that the “Family Guy” opening credits pay homage to “All in the Family”  Mr. MacFarlane said he tried to include two to three episodes each season that are issue-oriented. When the topic of abortion came up in the “Family Guy” writers’ room, he said, “There’s nothing about that issue that should be any different than doing an episode about gay marriage or an episode about the oil spill.”

In the script that Mr. Smith delivered, Lois Griffin, the wife of the titular “Family Guy” lummox, Peter Griffin, agrees to be a surrogate mother for a college friend who cannot conceive. When the friend and her husband are killed in a car accident, Lois debates whether she should keep the child, frequently finding herself in opposition to Peter’s wishes.

Mr. Smith, who describes himself as “a recovering Catholic,” said the script was not especially contentious when it was revised by the show’s mostly male writing staff. “We’ve had more spirited debates about whether or not we should state whether Santa Claus is real,” Mr. Smith said.

When Mr. MacFarlane presented the concept to Fox, it warned him that the subject matter raised a red flag, but allowed him to produce the episode anyway. He said he believed that the network would eventually run it, as it had an earlier episode called “When You Wish Upon a Weinstein” that it rejected in 2000. That installment, in which Peter yearns for his son Chris to become smarter by converting to Judaism, was first shown on Adult Swim on Cartoon Network in 2003, and then on Fox in 2004. (“Nobody got too offended,” Mr. MacFarlane said. “Most of the time these things turn out to be nothing.”)

But the Fox network decided not to show “Partial Terms of Endearment.” The network said in a statement that it fully supported “the producers’ right to make the episode and distribute it in whatever way they want,” and declined to elaborate on its decision. A spokeswoman for Adult Swim also said in an e-mail message that there were “no plans to air that episode of ‘Family Guy.’ ”

Last August Kevin Reilly, Fox’s entertainment president, told reporters at the Television Critics Association tour that the rejection of the episode “was a business decision” because it represented “fragile subject matter at a sensitive time.” But the “Family Guy” staff remains unclear on Fox’s rationale.

On one level the “Family Guy” producers understand that some of their jokes  a scene in which Lois is impregnated by Peruvian natives wielding blow-dart guns; a lengthy Warner Brothers parody in which Peter stalks Lois with an Acme Miscarriage Kit  may not have treated the abortion debate with proper gravity.

But they say there is no way to predict what material will offend audiences. Mr. Smith pointed to an episode in which the family dog, Brian, becomes an advocate for marijuana legalization.

“I have two sons,” Mr. Smith said, “and I don’t know if I feel comfortable with this cartoon dog telling people that life is better with a bag of weed.” Mr. Smith said more viewers complained about a scene in which Peter accidentally kills a neighbor’s cat.

There was also support from Twentieth Century Fox Home Entertainment, which felt that issues of taste would not discourage “Family Guy” fans from seeking the episode on DVD, and determined that DVD sales could cover the production costs of “Partial Terms of Endearment” if the network did not broadcast it.

“Seth and I have had arguments where I’m the nervous Nellie, and he’s pushing the envelope,” said Mike Dunn, the president of Fox’s home entertainment unit. “Finally it’s like, O.K., you win. This franchise does better when it’s pushed.”

Mr. MacFarlane said that the word abortion may simply be a “comedy red zone that you just shouldn’t enter,” noting that Fox had also made him change a joke because it contained the phrase World Trade Center.

But he did not criticize Fox for its decisions, which he said revealed more about mass audiences than about the networks.

“People in America, they’re getting dumber,” Mr. MacFarlane said. “They’re getting less and less able to analyze something and think critically, and pick apart the underlying elements. And more and more ready to make a snap judgment regarding something at face value, which is too bad.”

Whatever Fox’s reasons for refusing to broadcast “Partial Terms of Endearment,” Mr. MacFarlane said it was unlikely that the decision came from the corporation’s politically conservative chairman, Rupert Murdoch.

“My assessment of him has always been that he is a shrewd businessman first and a conservative second,” Mr. MacFarlane said, adding: “If he felt that something like this would be profitable to the corporation, he would have no issue airing it.”

Meanwhile, Mr. Smith joked that he was more worried about what the loss of network residuals for the episode would mean for his own bottom line.

“I have two kids in private school, man,” he said. “Fox is hitting me where it hurts. I’m always going to have a creative outlet here, but jeez, don’t take my money away.”

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Arts »A version of this article appeared in print on July 20, 2010, on page C1 of the New York edition.